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Guiding-center recursive Vlasov and Lie-transform methods in plasma physics

Published online by Cambridge University Press:  01 October 2009

A. J. BRIZARD  and
A. MISHCHENKO
A. J. BRIZARD
Affiliation:
Department of Physics, Saint Michael's College, Colchester, VT 05439, USA (abrizard@smcvt.edu)
A. MISHCHENKO
Affiliation:
Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-17491, Greifswald, Germany
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Abstract

The gyrocenter phase-space transformation used to describe nonlinear gyrokinetic theory is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The present work clarifies the relation between the derivation of the gyrocenter phase-space coordinates by the guiding-center recursive Vlasov method and the method of Lie-transform phase-space transformations.

Type
Papers
Information
Journal of Plasma Physics , Volume 75 , Issue 5 , October 2009 , pp. 675 - 696
Copyright
Copyright © Cambridge University Press 2009

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References

[1]Brizard, A. J. 2000 New variational principle for the Vlasov–Maxwell equations. Phys. Rev. Lett. 84, 5768–5771.CrossRefGoogle ScholarPubMed
[2]Brizard, A. J. 2000 Variational principle for nonlinear gyrokinetic Vlasov–Maxwell equations. Phys. Plasmas 7, 4816–4822.CrossRefGoogle Scholar
[3]Brizard, A. J. and Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory. Rev. Mod. Phys. 79, 421–468.CrossRefGoogle Scholar
[4]Catto, P. J. 1978 Linearized gyrokinetics. Plasma Phys. 20, 719–722.CrossRefGoogle Scholar
[5]Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic Press, New York.Google Scholar
[6]Dimits, A. M., LoDestro, L. L. and Dubin, D. H. E. 1992 Gyroaveraged equations for both the gyrokinetic and drift-kinetic regimes. Phys. Fluids B 4, 274–277.CrossRefGoogle Scholar
[7]Dubin, D. H. E., Krommes, J. A., Oberman, C. and Lee, W. W. 1983 Nonlinear gyrokinetic equations. Phys. Fluids 26, 3524–3535.CrossRefGoogle Scholar
[8]Frieman, E. A. and Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502–508.CrossRefGoogle Scholar
[9]Hastie, R. J., Taylor, J. B. and Haas, F. A. 1967 Adiabatic invariants and the equilibrium of magnetically trapped particles. Ann. Phys. (NY) 41, 302–338.CrossRefGoogle Scholar
[10]Hinton, F. L. and Hazeltine, R. D. 1976 Theory of plasma transport in toroidal confinement systems. Rev. Mod. Phys. 48, 239–308.CrossRefGoogle Scholar
[11]Parra, F. I. and Catto, P. J. 2008 Limitations of gyrokinetics on transport time scales. Plasma Phys. Control. Fusion 50, 065014.CrossRefGoogle Scholar
[12]Rutherford, P. H. and Frieman, E. A. 1968 Drift instabilities in general magnetic field configurations. Phys. Fluids 11, 569–585.CrossRefGoogle Scholar
[13]Taylor, J. B. 1967 Magnetic moment under short-wave electrostatic perturbations. Phys. Fluids 10, 1357–1359.CrossRefGoogle Scholar